Question

a triangle has one side of length 12 and another of length 7 which of the following are possible lengths of the third side ​

Answer 1

7 and 12

Explanation:

using triangle inequality theorem

if triangle has side a,b, and c, then all of them will trus if fulfill this inequality

a+b > c

a+c > b

b+c > a

now take a = 7 and b = 12

so the number c which can make triangle with a and b is

7 and 12

Answer 2

Explanation:

The first rule is that 2 of the sides must be bigger than the third.

4 and 7 makes 11 which is not bigger than 12, so A is not an answer.

5 + 7 = 12 That does not exceed 12, so the second one is not an answer

12 12 and 7 works perfectly. It makes an isosceles triangle. Any two of the three sides added together is larger than the third side.

If you put 19 20 or 21 into what you think might make a triangle, you would be incorrect. 12 and 7 makes 19. 19 is too large because 12 and 7 will lie flat on 19. No triangle works.

So only 12 works.

In short, 5<x<19 will create a triangle. Anything outside that inequality will not.